相关论文: A characterization of the dynamics of Schr\"oder's…

We propose an efficient, accurate method to integrate the basins of attraction of a smooth function defined on a general discrete grid, and apply it to the Bader charge partitioning for the electron charge density. Starting with the…

A new variant of Newton's method - named Backtracking New Q-Newton's method (BNQN) - which has strong theoretical guarantee, is easy to implement, and has good experimental performance, was recently introduced by the third author.…

We consider a system of coupled nonlinear Schr{\"o}dinger equations in one space dimension. First, we prove the existence of multi-speed solitary waves, i.e solutions to the system with each component behaving at large times as a solitary…

Motivated by recent experimental studies of matter-waves and optical beams in double well potentials, we study the solutions of the nonlinear Schr\"{o}dinger equation in such a context. Using a Galerkin-type approach, we obtain a detailed…

The method of solving of nonlinear Schr\"odinger equation is considered. Some examples of its applications are demonstrated.

An efficient method is proposed for numerical solutions of nonlinear Schr\"{o}dinger equations in an unbounded domain. Through approximating the kinetic energy term by a one-way equation and uniting it with the potential energy equation,…

We investigate Newton's method as a root finder for complex polynomials of arbitrary degree. While polynomial root finding continues to be one of the fundamental tasks of computing, with essential use in all areas of theoretical…

Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the last years. However, the polynomial case has not been…

The asymptotic iteration method is used to find exact and approximate solutions of Schroedinger's equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent).…

We consider a class of nonlinear Schrodinger equation in four and five space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in L2)…

The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schr\"odinger equations, which incorporate the cross-phase modulation,…

The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. We show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix…

We investigate bright solitons in the one-dimensional Schr\"odinger equation in the framework of an extended variational approach. We apply the latter to the stationary ground state of the system as well as to coherent collisions between…

A chirped parametrically driven discrete nonlinear Schrodinger equation is discussed. It is shown that the system allows two resonant excitation mechanisms, i.e., successive two-level transitions (ladder climbing) or a continuous…

This paper's aim is threefold. First, using Feynman's path approach to the derivation of theclassical Schr{\"o}dinger's equation in [6] and by introducing a slight path (or wave) dependency ofthe action, we derive a new class of equations…

This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…

In applied sciences, such as physics and biology, it is often required to model the evolution of populations via dynamical systems. In this paper, we focus on the problem of approximating the basins of attraction of such models in case of…

A multidomain spectral method with compactified exterior domains combined with stable second and fourth order time integrators is presented for Schr\"odinger equations. The numerical approach allows high precision numerical studies of…

Exact solutions for laminar stratified flows of Newtonian/non-Newtonian shear-thinning fluids in horizontal and inclined channels are presented. An iterative algorithm is proposed to compute the laminar solution for the general case of a…

We identify that for a broad range of parameters a variant of the soliton solution of the one-dimensional non-linear Schr\"{odinger} equation, the {\it breather}, is distinct when one studies the associated space curve (or soliton surface),…